[1]}.

If \(\mu \in {P}(\mathbb {R} )\)  and \(G_\mu \)  is the pseudo-inverse of its CDF \(F_\mu \) , then \((G_\mu )_\#({L}\upharpoonright [0,1])=\mu \) , where \({L}\)  is the Lebesgue measure.

The psuedo-inverse is an important tool for us to construct a particular coupling.
